A sensor is a device that receives signals of various types, for example electromagnetic signals such as heat or radio signals, or signals such as sound waves. There are passive sensors that only receive signals, and active sensors that send out a signal that is reflected against an object and thereafter returns to the sensor where the signal is read off. An active sensor can calculate distance and bearing of an object, for example by measuring the time it takes for a pulse signal to return and by using a directional antenna. The passive or active sensor has predetermined specific characteristics.
A further type of sensor is an adaptive sensor, which can be caused to change its characteristics depending upon how an object behaves, for example to increase the sweep frequency or the intensity, over a particular area within the range of the sensor.
A radar is a typical sensor as above, intended to detect targets and track targets using electromagnetic waves. The following description of the background art refers principally to radar, but as other sensors can also be used, the term sensor is used instead of radar.
A sensor's measurement characteristics are often described as a number of performance parameters:    pfa=the probability of false alarms per scan in a particular partial area,    pss=detection probability per scan (the subscript ss refers to single scan) for targets with a particular target area,    R=measurement accuracy, here expressed as a covariance matrix, and    T=detection time for the sensors search area.
From these parameters the sensor's average measurement rate (or effective measurement rate),
      1          T      e        ,can be calculated as
      1          T      e        =            p              s        ⁢                                  ⁢        s              T  
The first three parameters, pfa, pss and R, often vary across the sensor's search area. The detection ability of the sensor can, for example, be given a value by calculating the distance from the sensor where the probability of detection is 0.5. This distance is often called R50ss. By means of this value, the sensor's detection characteristics can be shown graphically by means of geometric figures in the form of circles or parts of circles where the value R50ss is scaled in such a way that the scaled value of R50ss constitutes the radius of the said figures, preferably together with a map of the area in question. The area that is described by the geometric figures is often called the sensor's range.
Certain existing planning tools (analysis tools) for sensors are based on ranges of the type described above and, in addition, can sometimes take into account topography and calculate restrictions in the range due to topographical masks by means of access to a map database.
A sensor's tracking characteristics can be described in a corresponding way as for the said detection characteristics, with a range R50aq given that a target approaches the sensor radially at a particular speed. This is described in Kronhamn T.R., “Surveillance Performance”, Radar '95, IEEE International Radar Conference, 1995, Washington, USA.
Problems arise when the performance of a system of sensors is to be calculated. The difficulty consists of obtaining an idea of the system's characteristics, in particular with respect to the tracking, when the sensors have greatly varying characteristics, not only with regard to the ranges but also with regard to other characteristics such as measurement rate, measurement accuracy and false alarms.
For tracking of targets measured by a plurality of sensors, the filtering of target data is already known. The two most common techniques are:                1. The sensors track the target separately and the result is thereafter fused.        2. The measurements are fused and a tracking filter is thereafter used on the resulting measurement.        
These methods relate to fusion of data in real systems, but can in principle also be applied for certain analysis analysis.
The filtering of target data according to point 1 comprises the calculation of a tracking filter, often a Kalman filter, for each sensor. For fusion of these values, the values in the filter's covariance matrix are to be fused, which involves laborious calculations that require a lot of data capacity and take a long time. A further problem is that in fusion of tracking data, the degree of correlation between the estimates is not known, which is not possible to calculate in real systems. In an analysis it should, however, be possible to calculate the correlations, but these calculations would add to the already laborious calculations.
In filtering target data according to point 2, a plurality of variants can arise, two of which variants (2a and 2b) will be illustrated in greater detail below. This is also described in Gan Q., Harris J.C., “Comparison of Two Measurement Fusion Methods for Kalman-filter Based Multisensor Data Fusion”, IEEE Trans on AES, Vol. 37, No. 1, pp 273–280, January 2001.
For fusion according to 2a, the fusion consists in the actual case of the measurement data being processed in the chronological order in which they are received, that is the contributions from the different sensors are received at different times and are processed by a common filter. This is, however, not applicable in the analytical case in which an evaluation of a system's performance is to be carried out. Actual measurement values are then not available, but only the general characteristics of the measurement values as described above. A fusion of these characteristics is to be carried out, but there are problems relating to randomness.
For fusion according to 2b, the measurements are fused before they are passed through a tracking filter. This can be carried out in two ways (2b1 and 2b2). In order to be able to utilise a filter according to 2b1, simultaneity is required for the measurements that are being fused. By simultaneity is meant here that the measurements are carried out at the same moment for all the sensors in the system and that there are no deviations in the measurement rate, detection characteristics or angle or distance to the measurement object. For use of a filter according to point 2b2 above, the measurements for the different sensors are weighted, fused, using known mathematical methods in which the accuracy of the weighted values, that is the variance, is calculated according to the equation (7-1) below.
                              R          j                =                              {                                          ∑                                  i                  =                  1                                                  N                  S                                            ⁢                                                          ⁢                              R                i                                  -                  1                                                      }                                -            1                                              (                  7          ⁢                      -                    ⁢          1                )            
This equation applies, however, only if the simultaneity described above is fulfilled, which in practice means that there are no deviations in measurement rate, detection characteristics or angle or distance to the measurement object. The probability of these criteria being fulfilled for a system of sensors that are tracking a mobile measurement object is very small, almost non-existent.
For fusion according to 2b2, the measurement vector is increased, instead of the measurement values being weighted and combined. In this case, the measurement contributions of the different sensors are added to a vector in sequence, with the result that a large measurement matrix is obtained which gives intensive calculations for calculating the tracking filter. In order to illustrate the problem, it can be mentioned that a measurement vector with n elements gives rise to a covariance matrix of n2 elements. Simultaneity is also required in the 2b2 case, with the problems mentioned above in the discussion concerning 2b1.
Some further disadvantages of existing technology are that only an idea of the measurement characteristics of the sensor(s) is obtained in the form of range and measurement accuracy. This is often combined with map databases in order to give an idea of the range of the sensor system, in the form of topographical masks and the like. These methods do not give performance for the sensor system as a whole, for example in the form of which tracking characteristics these measurement characteristics can be expected to provide.
There is a requirement to be able to carry out an analysis of sensor performance for a system of sensors, for planning the positioning of sensors in a particular area to be monitored. Sensor performance is normally calculated and described during design and purchasing. There is in addition an increasing need:                to evaluate necessary sensor resources (or alternatively, how existing resources are best to be utilised), in planning an assignment in which sensors are to be used,        to match the sensor resources to the situation in question in real time; so called reactive searching,        to evaluate the effect of possible or proposed measures/changes for adaptive sensors, both as automatic and manual “decision supports”.        
Further disadvantages of previously known technology are that the requirements that are described above cannot be fulfilled by previously known analysis methods.